Model-Checking of Infinite Kripke Structures Defined by Simple Graph Grammars

Embedded System Design is becoming a field of choice for Model-Driven Engineering techniques. On the engineering side, models bring an abstraction of the code that can then be generated (and regenerated) at will. On the semantic side, they bring a reasoning framework to guarantee or verify properties on the generated code. We focus here on the Clock Constraint Specification Language, initially defined as a companion language of the uml Profile for marte. More specifically, we propose a state-based data-structure inspired by lazy evaluation technique to represent the unbounded ccsl operators. Lazy evaluation allows for an intentional representation of infinite transition systems. We provide an algorithm to compute the synchronized product of such transition systems. Even though the transition systems are infinite, the result of the composition may become finite, in which case the (semi)algorithm terminates and exhaustive analysis becomes possible. We also study the time complexity and show that it is exponential in the number of clocks. We then explore several solutions where this worst-case estimation is not attained and where analyses have a much better complexity in practice.

An interactive theorem proving method for the verification of infinite state transition systems is described.

Deadlock-free output feedback controller design based on approximately abstracted observers

Given two pushdown automata, the bisimilarity problem asks whether the infinite transition systems they induce are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIME-hardness, which was the best previously known lower bound for this problem. Our lower bound result holds for normed pushdown automata as well.

In this paper, we design a symbolic output feedback controller of a cyber-physical system (CPS). The physical plant is modeled by an infinite transition system. We consider the situation that a finite abstracted system of the physical plant, called a c-abstracted system, is given. There exists an approximate alternating simulation relation from the c-abstracted system to the physical plant. A desired behavior of the c-abstracted system is also given, and we have a symbolic state feedback controller of the physical plant. We consider the case where some states of the plant are not measured. Then, to estimate the states with abstracted outputs measured by sensors, we introduce a finite abstracted system of the physical plant, called an o-abstracted system, such that there exists an approximate simulation relation. The relation guarantees that an observer designed based on the state of the o-abstracted system estimates the current state of the plant. We construct a symbolic output feedback controller by composing these systems. By a relation-based approach, we proved that the controlled system approximately exhibits the desired behavior.

We propose an algebraic semantics for the temporal logic CTL* and simplify it for its sublogics CTL and LTL. We abstractly represent state and path formulas over transition systems in Boolean left quantales. These are complete lattices with a multiplication that preserves arbitrary joins in its left argument and is isotone in its right argument. Over these quantales, the semantics of CTL* formulas can be encoded via finite and infinite iteration operators; the CTL and LTL operators can be related to domain operators. This yields interesting new connections between representations as known from the modal μ-calculus and Kleene/ω-algebra.

In this chapter, we introduce the two classes of discrete-time dynamical systems that we will focus on in the rest of the book: piecewise affine control systems with polytopic parameter uncertainties and switched linear systems. As particular instantiations of the first class, we define autonomous systems, fixed parameter systems, and combinations of the above. We define embeddings of such systems into (infinite) transition systems. This enables formal definitions for their semantics and the use of abstractions to map analysis and control problems for such systems to verification and synthesis problems for finite transition systems.

T-systems are generalisations of marked graph Petri nets. This paper describes synthesis algorithms that allow bounded or unbounded T-systems to be derived from finite or infinite labelled transition systems satisfying a set of necessary properties. These properties can thus be interpreted as axioms characterising T-system state spaces.

Verification is a hard task, but much progress has been achieved recently. Many verification problems have been shown decidable by reducing them to model-checking finite state transition systems. Verification of infinite state transition systems has achieved tremendous progress too, by showing that many particular cases were themselves decidable, such as timed automata [1] or some forms of pushdown-automata [4]. However, the demand for verification is growing fast, and the industrial needs go far beyond the verification of decidable systems.

Translating Controlled Graph Grammars to Ordinary Graph Grammars

Using graph transformation as a formalism to specify access control has several advantages, from the intuition provided by the visual aspect to the precise semantics and the systematic verification of constraints. Graph Transformations provide a uniform and precise framework for the specification of access control policies. After reviewing the basic notations of graph transformation, this article presents specification formalisms for workflow delegation policies using graph transformation. The authorization states are represented by graphs and state transition by graph transformation. The proposed formalization provides an intuitive description for the manipulation of graph structures as they occur in workflow delegation and a precise specification of consistency conditions on graphs and graph transformations. We specifies a type graph to represents the type information in the graph transformation for workflow delegation, a set of rules to build the system states and sets of positive and negative constraints to specify wanted and unwanted framework.

Specifying and programming with the help of agent systems is gaining more and more interest, especially in the field of distributed and reactive systems. In this paper, we propose a formal model of agent systems based on graph transformation. It is quite natural to visualize systems, especially system states, by means of graphs. Hence, it is also appropriate to specify those systems using graphs. Accordingly, changes from one state into another can be modeled by graph transformation.

Motivated by the work which has been done for Petri-nets, the paper presents a categorical approach to graph grammars “in the large”. In the large means, that we define categories of graph grammars, graph transition systems, and graph derivation systems which embody the notion “grammar”, “direct derivation”, and “derivation”, respectively, as they are defined in the classical algebraic theory. For this purpose we introduce a suitable notion of graph grammar morphism on “typed graph grammars” in analogy to Petri-nets. A typed graph grammar is a grammar for typed graphs which is a slight generalization of the standard case. The main result shows that the three categories are related by left-adjoint functors. We discuss the relationship of our results to similar results obtained in the Petri-net field, and applications to entity/relationship models.

Graph transformation has recently become more and more popular as a general, rule-based visual specification paradigm to formally capture (a) requirements or behavior of user models (on the model-level), and (b) the operational semantics of modeling languages (on the meta-level) as demonstrated by benchmark applications around the Unified Modeling Language (UML). The current paper focuses on the model checking-based automated formal verification of graph transformation systems used either on the model-level or meta-level. We present a general translation that inputs (i) a metamodel of an arbitrary visual modeling language, (ii) a set of graph transformation rules that defines a formal operational semantics for the language, and (iii) an arbitrary well-formed model instance of the language and generates a transitions system (TS) that serve as the underlying mathematical specification formalism of various model checker tools. The main theoretical benefit of our approach is an optimization technique that projects only the dynamic parts of the graph transformation system into the target transition system, which results in a drastical reduction in the state space. The main practical benefit is the use of existing back-end model checker tools, which directly provides formal verification facilities (without additional efforts required to implement an analysis tool) for many practical applications captured in a very high-level visual notation. The practical feasibility of the approach is demonstrated by modeling and analyzing the well-known verification benchmark of dining philosophers both on the model and meta-level.

In this paper, we investigate transition systems of a class of Petri nets suitable for the modelling and behavioural analysis of globally asynchronous locally synchronous systems. The considered model of Elementary Net Systems with Localities (ENL-systems) is basically that of Elementary Net Systems (EN-systems) equipped with an explicit notion of locality. Each locality identifies a distinct set of events which may only be executed synchronously, i.e., in a maximally concurrent manner. For this reason, the overall behaviour of an ENL-system cannot be represented by an interleaved transition system, with arcs being labelled by single events, but rather by a suitable notion of a step transition system, with arcs being labelled by sets of events executed concurrently.We completely characterise transition systems which can be generated by Elementary Net Systems with Localities under their intended concurrency semantics. In developing a suitable characterisation, we follow the standard approach in which key relationships between a Petri net and its transition system are established via the regions of the latter defined as specific sets of states of the transition system. We argue that this definition is insufficient for the class of transition systems of ENL-systems, and then augment the standard notion of a region with some additional information, leading to the notion of a region with explicit input and output events (or io-region).We define, and show consistency of, two behaviour preserving translations between ENL-systems and their transition systems. As a result, we provide a solution to the synthesis problem of Elementary Net Systems with Localities, which consists in constructing an ENL-system for a given transition system in such a way that the transition system of the former is isomorphic to the latter.KeywordsTheory of concurrencyPetri netselementary net systemslocalitiesanalysis and synthesisstep sequence semanticsstructure and behaviour of netstheory of regionstransition systems